Algebraic monodromy and obstructions to formality

TL;DR

This paper explores the relationship between algebraic monodromy, fiber properties, and formality in fibrations over the circle, providing new criteria for space and group formality with applications in topology and singularity theory.

Contribution

It introduces a general result on iterated group extensions and applies it to derive novel criteria for the formality of spaces and 1-formality of groups.

Findings

New criteria for space and group formality

Applications to low-dimensional topology and singularity theory

General results on iterated group extensions

Abstract

Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more general result about iterated group extensions. As an application, we obtain new criteria for formality of spaces, and 1-formality of groups, illustrated by bundle constructions and various examples from low-dimensional topology and singularity theory.